Bayesian Computation Meets Topology

Julius von Rohrscheidt, Bastian Rieck, Sebastian M Schmon

Abstract:

Computational topology recently started to emerge as a novel paradigm for characterising
the ‘shape’ of high-dimensional data, leading to powerful algorithms in (un)supervised
representation learning. While capable of capturing prominent features at multiple scales,
topological methods cannot readily be used for Bayesian inference. We develop a novel
approach that bridges this gap, making it possible to perform parameter estimation in a
Bayesian framework, using topology-based loss functions. Our method affords easy integration
into topological machine learning algorithms. We demonstrate its efficacy for parameter
estimation in different simulation settings.

Submission Length: Regular submission (no more than 12 pages of main content)

Code: https://github.com/aidos-lab/TABAC

Assigned Action Editor: ~Patrick_Flaherty1

Submission Number: 3097